A catalytic secondary reforming process, for the production of synthesis gas, comprises the successive steps of: feeding a first gas flow comprising hydrocarbons and a second gas flow comprising oxygen into a reforming reactor, at least one of such gas flows being fed into the reactor in a predetermined feed direction substantially parallel, preferably coaxial, to a longitudinal axis of the reactor, mixing the gas flows in the reactor, with substantially simultaneous oxidation of the hydrocarbons of the first gas flow by the oxygen of the second flow.